Brazilian Journal of Probability and Statistics

Yaglom limit via Holley inequality

Abstract

Let ${S}$ be a countable set provided with a partial order and a minimal element. Consider a Markov chain on $S\cup\{0\}$ absorbed at $0$ with a quasi-stationary distribution. We use Holley inequality to obtain sufficient conditions under which the following hold. The trajectory of the chain starting from the minimal state is stochastically dominated by the trajectory of the chain starting from any probability on ${S}$, when both are conditioned to nonabsorption until a certain time. Moreover, the Yaglom limit corresponding to this deterministic initial condition is the unique minimal quasi-stationary distribution in the sense of stochastic order. As an application, we provide new proofs to classical results in the field.

Article information

Source
Braz. J. Probab. Stat., Volume 29, Number 2 (2015), 413-426.

Dates
First available in Project Euclid: 15 April 2015

https://projecteuclid.org/euclid.bjps/1429105595

Digital Object Identifier
doi:10.1214/14-BJPS269

Mathematical Reviews number (MathSciNet)
MR3336873

Zentralblatt MATH identifier
1321.60142

Citation

Ferrari, Pablo A.; Rolla, Leonardo T. Yaglom limit via Holley inequality. Braz. J. Probab. Stat. 29 (2015), no. 2, 413--426. doi:10.1214/14-BJPS269. https://projecteuclid.org/euclid.bjps/1429105595

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